Let $\mathbb { R }$ denote the set of all real numbers. For a real number $x$, let $[ x ]$ denote the greatest integer less than or equal to $x$. Let $n$ denote a natural number.

Match each entry in List-I to the correct entry in List-II and choose the correct option.

\section*{List-I}
(P) The minimum value of $n$ for which the function

$$f ( x ) = \left[ \frac { 10 x ^ { 3 } - 45 x ^ { 2 } + 60 x + 35 } { n } \right]$$

is continuous on the interval $[ 1,2 ]$, is\\
(Q) The minimum value of $n$ for which

$$g ( x ) = \left( 2 n ^ { 2 } - 13 n - 15 \right) \left( x ^ { 3 } + 3 x \right)$$

$x \in \mathbb { R }$, is an increasing function on $\mathbb { R }$, is\\
(R) The smallest natural number $n$ which is greater than 5, such that $x = 3$ is a point of local minima of

$$h ( x ) = \left( x ^ { 2 } - 9 \right) ^ { n } \left( x ^ { 2 } + 2 x + 3 \right) ,$$

is\\
(S) Number of $x _ { 0 } \in \mathbb { R }$ such that

$$l ( x ) = \sum _ { k = 0 } ^ { 4 } \left( \sin | x - k | + \cos \left| x - k + \frac { 1 } { 2 } \right| \right) ,$$

$x \in \mathbb { R }$, is NOT differentiable at $x _ { 0 }$, is

\section*{List-II}
(1) 8\\
(2) 9\\
(3) 5\\
(4) 6\\
(5) 10

\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
(A) & $( \mathrm { P } ) \rightarrow ( 1 )$ & $( \mathrm { Q } ) \rightarrow ( 3 )$ & $( \mathrm { R } ) \rightarrow ( 2 )$ & $( \mathrm { S } ) \rightarrow ( 5 )$ \\
\hline
(B) & $( \mathrm { P } ) \rightarrow ( 2 )$ & $( \mathrm { Q } ) \rightarrow ( 1 )$ & $( \mathrm { R } ) \rightarrow ( 4 )$ & $( \mathrm { S } ) \rightarrow ( 3 )$ \\
\hline
(C) & $( \mathrm { P } ) \rightarrow ( 5 )$ & $( \mathrm { Q } ) \rightarrow ( 1 )$ & $( \mathrm { R } ) \rightarrow ( 4 )$ & $( \mathrm { S } ) \rightarrow ( 3 )$ \\
\hline
(D) & $( \mathrm { P } ) \rightarrow ( 2 )$ & $( \mathrm { Q } ) \rightarrow ( 3 )$ & $( \mathrm { R } ) \rightarrow ( 1 )$ & $( \mathrm { S } ) \rightarrow ( 5 )$ \\
\hline
\end{tabular}
\end{center}